Stress relaxation was studied in torsion under superposed hydrostatic pressure using a newly constructed device. Combination of these measurements with the determination of expansivities and compressibilities and with earlier measurements of stress relaxation in tension leads to verification of the description of the combined effects of temperature and pressure on shear relaxation by an extension of the classical free volume theory. The predictions of an extension of the Adam-Gibbs theory to the pressure domain are also compared with the data. This theory is not as successful in predicting superposition. The data are also examined in light of an adaptation of the Simha-Somcynsky equation of state to the free volume theory. Prediction of the effect of pressure by the theory requires a single adjustable parameter. It was possible to calculate the free volume parameters of several polymers without use of information from high pressure experiments.